Spin effects in ultrafast laser-plasma interactions

Abstract

Ultrafast laser pulses interacting with plasmas can give rise to a rich spectrum of physical phenomena, which have been extensively studied both theoretically and experimentally. Less work has been devoted to the study of polarized plasmas, where the electron spin may play an important role. In this short review, we illustrate the use of phase-space methods to model and simulate spin-polarized plasmas. This approach is based on the Wigner representation of quantum mechanics, and its classical counterpart, the Vlasov equation, which are generalized to include the spin degrees of freedom. Our approach is illustrated through the study of the stimulated Raman scattering of a circularly polarized electromagnetic wave interacting with a dense electron plasma.

Vlasov–Maxwell equations with spin effects

“…Hence, this bracket is not strictly speaking a Poisson bracket such as the one occurring in the scalar model; nevertheless, we will still refer to it as a Poisson bracket for the sake of simplicity. We note that the case β = 1, γ = 1 and α = 3 yields the vector model introduced in (Hurst et al 2014(Hurst et al , 2017Manfredi et al 2022) and ensures, by Proposition 1, the equivalence between the two models.…”

“…Furthermore, the vector model enjoys a geometric (antisymmetric-bracket) structure when β + 2γ = α. The choice β = 1, γ = 1 and α = 3 satisfies both conditions, and recovers the 'standard' vector model commonly used in the literature (Hurst et al 2014(Hurst et al , 2017Manfredi et al 2022). However, as the γ -term is difficult to implement in a PIC method because of the double derivative, it has been common to take γ = 0 when simulating the scalar model (Crouseilles et al 2021).…”

“…In this section, we recall the governing equations for the scalar spin Vlasov-Maxwell system in the extended phase space (x, p, s) (see Marklund et al 2010;Zamanian et al 2010;Marklund & Morrison 2011;Manfredi et al 2019) and the corresponding vector system in the standard phase space (x, p) (see Hurst et al 2014Hurst et al , 2017Manfredi, Hervieux & Crouseilles 2022). Both models are semiclassical approximations, in the sense that the orbital motion is treated with classical trajectories, whereas the spin degrees of freedom are fully quantum.…”

“…Full vector model with γ = 0. In this last part, we simulate the full spin-Vlasov-Maxwell vector model introduced in Hurst et al (2014Hurst et al ( , 2017 and Manfredi et al (2022), i.e. for γ = 1, α = 3, β = 1, for which we cannot perform simulations for the scalar model, since the cross-derivative term is not implemented in our PIC code.…”

“…2019) and the corresponding vector system in the standard phase space (see Hurst et al. 2014, 2017; Manfredi, Hervieux & Crouseilles 2022). Both models are semiclassical approximations, in the sense that the orbital motion is treated with classical trajectories, whereas the spin degrees of freedom are fully quantum.…”